Difference: 20151129_MSciSpectrocopyLab (10 vs. 11)

Revision 1112 Sep 2016 - AshleaKemp

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META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

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  • Finally a quadratic term was fitted for the background of the image, which has the equation:
\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
  • These are plotted below
Changed:
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3Fits.png
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3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
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3Fit_Back.png
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3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
Line: 76 to 76
 
 \begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
Changed:
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VegaFit.png
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VegaFit.png
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 -1.48(1.39e05)
Line: 122 to 122
 
$\chi^2$ per dof 1587 968 969

  • Some of the grating setting are shown below
Changed:
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0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
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0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
 

Halogen Lamp

  • For the halogen lamp the above fit parameters were used to set the wavelength of each frame, these were then plotted as shown below:
  • The below plot shows the linear and squared plots and it can clearly be seen to improve at larger and smaller wavelengths, however not much change in the center.
Changed:
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LinearSquare.png
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LinearSquare.png
 
  • When the cubed parameters were used, the plot did no seem to improve, as the image shows
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Cubed.png
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Cubed.png
 
  • This may be due to an incorrect point which the cubed plot fits better to however is further from the true value
-- AshleaKemp - 27 Nov 2015
 
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